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These knowledge and skills will help you understand the different geometric relationships involving tangents and secants of a circle. As you go through this lesson, think of this important question: How do the different geometric relationships involving tangents and secants of a circle facilitate finding solutions to real-life problems and making wise decisions? To find the answer, perform each activity. If you find any difficulty in answering the exercises, seek the assistance of your teacher or peers or refer to the modules you have studied earlier.

You may check your work with your teacher. Perform the following activity. Answer every question that follows. Procedure: 1. Use a compass to draw S. Draw line m such that it intersects S at exactly one point.

Label the point of intersection as T. Connect S and T with a line segment. What is TS in the figure drawn?

Mark four other points on line m such that two of these points are on the left side of T and the other two points are on the right side. Label these points as M, N, P, and Q, respectively. How do the measures of the four angles compare? Repeat steps 2 to 5. This time, draw line n such that it intersects the circle at another point. What statement can you make about the measures of angles in item 5 and digltal in item 6?

How do the lengths of the five segments compare? What do you think is the shortest segment from the center of a circle to the line that intersects it at exactly one point? Explain your answer. In the activity you have just done, were you able to compare the measures of different angles drawn? Were you able to determine the shortest segment from the center of a circle to the line that intersects it at exactly one point? I know you were! The activity you have done has something to do with your new lesson.

Do you know why? Find this out in the succeeding activities! In the figure below, C is the center of the circle. Use the figure to answer the questions that follow. Which lines intersect circle Measure king digital tape measure diagram at two points? How about the lines that intersect the circle at exactly one point? What are the angles having A as the vertex? Dagram as the vertex?

D as the vertex? G as the vertex? Make a list of these angles, then describe each. How would kihg determine the measures of the arcs intercepted by the angles? Give the degree measure of each arc. Were you able to measure the different angles and arcs shown in the figure?

Were you able to find out the different relationships among these angles and arcs? Learn more about these relationships in the succeeding activities. Prepare the following materials, then perform the activity that follows. Answer every question asked. Materials: Diaagram cardboard with radius 6 cm that is equally divided into measuer arcs so that each arc measures 5.

Attach the endpoints of the strings to R the cardboard or kkng flat surface using self-adhesive tape to form an S angle of any convenient measure. Label the angle kong RST. Locate the center of the circular R 2. Slide it underneath the strings until its center coincides with their point of intersection, S. If the edge of the circular cardboard represents a circle, what is RST in relation to the circle?

Explain how you arrived at your answer. Mark and label another point V measure king digital tape measure diagram the circle. Describe the relationship, if there is any.

Was the activity interesting? Were you able to come up with some relationships involving angles formed by lines and their intercepted arcs? Are you ready to learn about tangents and secants and their real-life applications? I am sure you are! How do the different geometric relationships involving tangents and secants of a circle facilitate finding solutions to real-life problems and making wise decisions?

You will find these out in the activities in the next section. Before doing these activities, read and understand first some important notes on tangents and secants and measure king digital tape measure diagram different geometric relationships involving them.

Understand measure king digital tape measure diagram well the examples presented so that you will be guided in doing the succeeding activities. A tangent to a circle is a line coplanar with the circle and intersects it in iing and diavram one measure king digital tape measure diagram. The point of intersection of the line and the circle is called the point of tangency.

PQ is a Q C tangent measure king digital tape measure diagram and A is the point of tangency. P Postulate on Tangent Line. At a given point on a circle, one and only one line can measure king digital tape measure diagram drawn that is tangent to the circle.

A To illustrate, consider V on the right. If U is a point on the circle, then one and only one U line can be drawn through U that is tangent to the circle. Theorems on Tangent Line B 1. If a line is tangent to a circle, then it is perpendicular to the radius drawn to the point of tangency. If a line is perpendicular to a radius of a circle at its endpoint that is on the circle, then the line is tangent to the circle.

If two segments from the same exterior point are tangent to a circle, then the two segments are congruent. A common tangent is a line that is tangent to two circles in the same plane. Common internal tangents Common external tangents do intersect the segment joining not intersect the segment joining the centers of the two circles the centers of the two circles.

Lines c and d are Lines s and t are common internal tangents. Tangent and Secant. Segments and rays that are contained in the tangent or intersect the circle in one and only one point are digigal said to be tangent to the circle.

A secant contains a chord of a circle. In circle A, MN is a secant line. If two secants intersect in the exterior of a circle, then the measure of the angle formed is one-half the positive difference of the measures of the intercepted arcs. If a secant and a tangent intersect in the exterior of a circle, then the measure of jing angle formed is one-half the positive difference of the measures of the intercepted arcs.

If two tangents intersect diagtam the exterior of a circle, then the measure of the angle formed is one-half the positive difference of the measures of the intercepted arcs. If two secants intersect in the interior of a circle, then the measure of an angle formed is one-half the sum of the measures of the arcs intercepted by the angle and its vertical angle. If a secant and a tangent intersect at the point of tangency, then the measure of each angle formed is one-half the measure of its intercepted measure king digital tape measure diagram. Your goal in this section is to apply the key concepts mewsure tangents and secants of a circle.

Use the mathematical ideas and the examples presented in the preceding section to answer the activities provided. Use the figure to answer the following questions. Which lines are tangent to the circle? Which lines are secants? At what points does each secant N intersect the circle? Q O L P How about the tangents? Which angles are formed by two M secant lines?

Name all the measure king digital tape measure diagram arcs in the figure. Which angles intercept each of these arcs? How about mNP? Were you able to identify the arcs measure king digital tape measure diagram these angles intercept? Were you able to determine the unknown measure of the angle? I am sure you were! In the next activity, you will further apply the different ideas learned about tangents and secants in finding the measures measure king digital tape measure diagram angles, arcs, and segments in some geometric figures.

Aug 18,  · "As a freshman at Mason, I had difficulties being on my own for the first time. During my senior year, I didn’t know what I wanted to do after graduation so, I ended up visiting the Career Services. ONTEL Measure King 3-in-1 Digital Tape Measure String Mode, Sonic Mode & Roller Mode As seen On Tv Visit the Ontel Store. out of 5 stars ratings. Price: $ & FREE Returns Return this item for free. Free returns are available for the shipping address you chose. You can return the item for any reason in new and unused condition: no /5(). Mar 20,  · Measure DC voltage at TP2 (WPC TP) on the Power/Driver board. DMM set to DC volts (if not an auto-ranging meter, expect to measure 5VDC) Black lead secured to game ground (the ground braid in the head is a good place to pick up ground) Red lead on TP2 (WPC TP). Remember the reading.

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